Resonant nonlinear magneto-optical effects in atomsâ - The Budker ...

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30 Transmission (%) Rotation angle φ (mrad) Wall-induced Ramsey effect B z ⩵ΜG Transit effect B z ⩵mG Laser detuning (GHz) (a) (b) FIG. 18 (a) Wall-induced Ramsey rotation spectrum obtained by Budker et al. (2000b) for light intensity 1.2 mW cm −2 and beam diameter ∼3 mm. (b) Transit effect rotation spectrum, for light intensity 0.6 mW cm −2 . (c) Light transmission spectrum for light intensity 1.2 mW cm 2 . Background slope in light transmission is due to change in incident laser power during the frequency scan. tensity and frequency at which highest magnetometric sensitivity is achieved, the sign of optical rotation is opposite of that obtained for the low light-power transit effect. Budker et al. (2000a) explained this as the effect of alignment-to-orientation conversion (Sec. V.C) due to the combined action of the optical electric field and the magnetic field. Skalla and Waeckerle (1997) studied the wall-induced Ramsey effect in cells with various geometries (cylindrical, spherical, and toroidal), and used spatially separated pump and probe fields to measure Berry’s topological phase (Berry, 1984). Yashchuk et al. (1999b) investigated the possibilities of applying the separated optical field method to improve the sensitivity of NMOR-based magnetometers XII.A. In addition to their application in precision magnetometry (Sec. XII.A), NMOE in paraffin-coated cells were investigated in relation to tests of fundamental symmetries (Sec. XII.B) and the study of light propagation dynamics (Sec. XIII.B). (c) 2. Theoretical analysis In order to obtain a theoretical description of NMOE in paraffin-coated cells, one must extend the density matrix calculation of Sec. VII.B to describe both the illuminated and non-illuminated regions of the cell, and the effects of velocity-mixing and spin exchange. Expressions for the effect of alkali-alkali spin-exchange on the density matrix have been obtained by Okunevich (1994, 1995); Valles and Alvarez (1994, 1996), following work of Grossetete (1965). When atomic orientation is nonzero, the expressions become nonlinear; thus, they are easily applied only for low-power linearly polarized pump light far from the conditions of alignment-to-orientation conversion (Sec. V.C). Taking velocity mixing and multiple cell regions into account is straightforward but computationally intensive. A detailed description of such a calculation and comparison with experiment is in preparation by D. Budker and coworkers. F. Gas discharge Gas discharge allows one to study ionized species, refractory materials, and transitions originating from metastable states, and has been extensively used in atomic spectroscopy and polarization studies in particular (as in the work of, for example, Aleksandrov and Kulyasov, 1972; Lombardi, 1969). In optogalvanic spectroscopy one detects light-induced transitions by measuring the changes in conductivity of a discharge. The optogalvanic method has been applied to the study of nonlinear level crossing and other NMOE (Hannaford and Series, 1981; Stahlberg et al., 1989). Other examples of NMOE work employing gas discharge are the study of Lowe et al. (1987), who used Zeeman quantum beats in transmission (i.e., time-dependent NMOR; see Sec. VIII.B) in a pulsed-pump, cw-probe experiment to determine polarization-relaxation properties of a Sm vapor produced in a cathode sputtering discharge, and that of Alipieva and Karabasheva (1999) who studied the nonlinear Voigt effect in the 2 3 P → 3 3 D transition in neutral He. G. Atoms trapped in solid and liquid helium A recent(and experimentally demanding) technique for reducing spin-relaxation is the trapping of the paramagnetic species under investigation in condensed (superfluid or solid) 4 He. Solid-rare-gas-matrix isolation spectroscopy (Coufal, 1984; Dunkin, 1998) has been extensively used by chemists in the past half-century for the investigation of reactive atoms, ions, molecules, and radicals. In all heavy-rare-gas matrices, however, the anisotropy of the local fields at individual atomictrapping sites causes strong perturbation of guest atom spin-polarization via spin-orbit interactions. As a conse-
31 quence, no high-resolution magneto-optical spectra have been recorded in such matrices. However, the quantum nature (large amplitude zero-point motion) of a condensed helium matrix makes it extremely compressible, and a single-valence-electron guest atom can impose its symmetry on the local environment via Pauli repulsion. Alkali atoms thus form spherical nanometer-sized cavities (atomic bubbles), whose isotropy, together with the diamagnetism of the surrounding He atoms, allows longlived spin polarization to be created in the guest atoms via optical pumping. With Cs atoms in the cubic phase of solid He, longitudinal spin relaxation times T 1 of 1 s were reported by Arndt et al. (1995), while transverse relaxation times T 2 are known to be larger than 100 ms (Kanorsky et al., 1996). The T 1 times are presumably limited by quadrupolar zero-point oscillations of the atomic bubble, while the T 2 times are limited by magnetic field inhomogeneities. In superfluid He, the coherence life times are limited by the finite observation time due to convective motion of the paramagnetic atoms in the He matrix (Kinoshita et al., 1994). Nonlinear magneto-optical level-crossing signals (the longitudinal and transverse ground-state Hanle effects) were observed by Arndt et al. (1995); Weis et al. (1995) as rather broad lines due to strong magnetic-field inhomogeneities. In recent years, spin-physics experiments in solid helium have used (radio-frequency/microwave– optical) double resonance techniques. Optical and magneto-optical studies of defects in condensed helium were reviewed by Kanorsky and Weis (1998). Applications of spin-polarized atoms in condensed helium include the study of the structure and dynamics of local trapping sites in quantum liquids/solids, and possible use of such samples as a medium in which to search for a permanent atomic electric-dipole moment (Weis et al. (1997); Sec. XII.B). H. Laser-cooled and trapped atoms Recently, atomic samples with relatively long spinrelaxation times were produced using laser-cooling and trapping techniques. When studying NMOE in trapped atoms, one must take into account the perturbation of Zeeman sublevels by external fields (usually magnetic and/or optical) involved in the trapping technique. Atoms can be released from the trapping potentials before measurements are made in order to eliminate such perturbations. 31 There have been several recent studies of the Faraday 31 Another point to consider is that Doppler broadening due to the residual thermal velocities of trapped atoms is smaller than the natural line width of the atomic transition. Therefore, in the low-power limit, optical pumping does not lead to formation of Bennett structures (Sec. V.A) narrower than the width of the transition. and Voigt effects using magneto-optical traps (MOTs). Isayama et al. (1999) trapped ∼10 8 85 Rb atoms in a MOT and cooled them to about 10 µK. Then a pump beam was used to spin-polarize the sample of cold atoms orthogonally to an applied magnetic field of ∼2 mG. Larmor precession of the atoms was observed by monitoring the time-dependent polarization rotation of a probe beam. The limiting factor in the observation time (∼11 ms) for this experiment was the loss of atoms from the region of interest due to free fall in the Earth’s gravitational field. Labeyrie et al. (2001) studied magneto-optical rotation and induced ellipticity in 85 Rb atoms trapped and cooled in a MOT that was cycled on and off. The Faraday rotation was measured during the brief time (∼8 ms) that the trap was off. The time that the MOT was off was sufficiently short so that most of the atoms were recaptured when the MOT was turned back on. Franke-Arnold et al. (2001) performed measurements of both the Faraday and Voigt effects (Sec. I) in an ensemble of cold 7 Li atoms. Optical rotation of a weak far-detuned probe beam due to interaction with polarized atoms was also used as a technique for non-destructive imaging of Bose-Einstein condensates (as in the work of, for example, Matthews, 1999). Narducci (2001) has recently begun to explore the possibility of measuring NMOE in cold atomic fountains. The experimental geometry and technique of such an experiment would be similar to the setup for Faraday- Ramsey spectroscopy described in Sec. VIII.C, but the time-of-flight between the pump and probe regions could be made quite long (a few seconds). With far-off-resonant blue-detuned optical dipole traps, one can produce alkali vapors with ground-state relaxation rates ∼0.1 Hz [for example, Davidson et al. (1995) observed such relaxation rates for ground-state hyperfine coherences]. Correspondingly narrow features in the magnetic-field dependence of NMOE should be observable. However, we know of no experiments investigating NMOE in far-off-resonant optical dipole traps. IX. MAGNETO-OPTICAL EFFECTS IN SELECTIVE REFLECTION 1. Linear effects The standard detection techniques in atomic spectroscopy are the monitoring of the fluorescence light and of the light transmitted through the sample. A complementary, though less often used technique is monitoring the light reflected from the sample or, more precisely, from the window-sample interface. The reflected light intensity shows resonant features when the light frequency is tuned across an atomic absorption line (Cojan, 1954). The technique was discovered by Wood (1909) and is called selective reflection spectroscopy. A peculiar feature of selective reflection spectroscopy was discovered after the advent of narrow-band tunable lasers: when the
Page 1 and 2: Resonant nonlinear magneto-optical
Page 3 and 4: 3 @Ω Σ Σ n n n gΜB @ M =
Page 5 and 6: 5 sublevels in each individual atom
Page 7 and 8: 7 (Barkov and Zolotorev, 1980; Robe
Page 9 and 10: 9 can be used for studies of collis
Page 11 and 12: 11 of quantum interference. In the
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Page 15 and 16: 15 effect. 15 Many experiments were
Page 17 and 18: 17 experiment of Gawlik et al. (197
Page 19 and 20: 19 Index of refraction Number of at
Page 21 and 22: 21 tical electric fields causes ato
Page 23 and 24: 23 frequency detuning from resonanc
Page 25 and 26: 25 Rotation angle (mrad) I
Page 27 and 28: 27 separation, as anticipated, but
Page 29: 29 Faraday rotation φ (mrad) 5 0
Page 33 and 34: 33 ization in the electric field (F
Page 35 and 36: 35 tically pump the atomic medium i
Page 37 and 38: 37 to consider the photon shot-nois
Page 39 and 40: 39 Photodiode signal (V) 10 8 6 4 2
Page 41 and 42: 41 Ω |a (a) (b) (c) Ω Ω ab |b
Page 43 and 44: 43 and phase, respectively. Another
Page 45 and 46: 45 Saprykin, G. I. Smirnov, and V.
Page 47 and 48: 47 Gawlik, W., 1994, in Modern Nonl
Page 49 and 50: 49 Nakayama, S., G. W. Series, and
Page 51: 51 2002a, Magnetic shielding, unpub

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